“Always the eyes watching you and the voice enveloping you. Asleep or awake, working or eating, indoors or out of doors, in the bath or in bed — no escape. Nothing was your own except the few cubic centimetres inside your skull.” — George Orwell. 1984

le frequenze delle note musicali – what are the frequencies of music notes?

An interesting problem has faced musical instrument makers for hundreds of years. To get a “perfect 5th” (the interval between A and the E above, say), we need to play a note which has 1.5 times the frequency of A.

On a violin (or viola or any fretless stringed instrument) this is possible, and we can play a beautiful, perfect E at 440 × 1.5 = 660 Hz. But notice (from the frequency table above) that a piano playing the same note will play E = 659.26 Hz [just a little flat!].

Around 400 years ago, keyboards (usually harpsichords and organs) were tuned for a particular key (say D major), so that all the instruments, especially strings, sounded “right” in that key. The harpsichord sounded great in that key, but pretty awful in other unrelated keys (say B flat).

Around the time of J. S. Bach, it was decided to tune keyboards so that the notes were evenly spaced. Then the keyboard could sound better in any key. This is called equal tempered tuning.

Unfortunately, it means all stringed instruments have to allow for the slight differences in tunings between instruments. Strings are usually happiest when playing with other strings only, for this reason.